<html><head></head><body>Rob LeGrand wrote:<br>
<blockquote type="cite" cite="mid:20010428005130.38527.qmail@web11002.mail.yahoo.com"><pre wrap="">That exact method is implemented in my simulation as Dodgson(m). My "Dodgson"<br>isn't exactly Dodgson's method; it simply takes whatever pairwise matrix is<br>calculated (whether margins, winning-votes, etc.) and sums each candidate's<br>column. The one with the lowest sum is elected. (Mike's "Minimize Overruling"<br>in <a class="moz-txt-link-freetext" href="http://groups.yahoo.com/group/election-methods-list/message/6433">http://groups.yahoo.com/group/election-methods-list/message/6433</a> is the same<br>as Dodgson(wv).) The "Dodgson" methods do very well in my SU simulations; in<br>fact, Dodgson(av) almost rivals Borda in SU.</pre>
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That is what I anticipated...<br>
<blockquote type="cite" cite="mid:20010428005130.38527.qmail@web11002.mail.yahoo.com"><pre wrap=""> Unfortunately, Dodgson methods do<br>poorly in criterion compliances. I believe all four of them fail independence<br>of clones and Smith, both of which are important to me.</pre>
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As I noted, you would have to sacrifice Smith if you are interested in higher SU.<br>
If Smith is more important than SU, then this is not the best method. As we know,<br>
there is a significant difference in opinion about which criteria are important.<br>
<br>
You could of course create a Smith compliant version, by eliminating non-Smith<br>
candidates before applying the method, though I doubt that would leave the method<br>
with any advantages over other methods (except simplicity of the calculations after<br>
the Smith set is determined).<br>
<br>
Not sure what, if anything, could be done about clones in this method.<br>
<br>
A sequential variant is also possible: Eliminate the candidate with highest cost.<br>
Strike both the rows and columns corresponding to that candidate from the<br>
pairwise matrix. Recalculate the costs, and eliminate the candidate with the highest<br>
cost among the remaining candidates. Repeat until one candidate is left. I haven't<br>
given much thought to this variant yet. Maybe, like my previous suggestion, it's<br>
already been tried.<br>
<blockquote type="cite" cite="mid:20010428005130.38527.qmail@web11002.mail.yahoo.com"><pre wrap=""> And Dodgson(av), the<br>best in SU, even fails Condorcet, just like most other "all-votes" methods.</pre>
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I don't know what "all-votes" methods are. Could you define this term for me?<br>
<blockquote type="cite" cite="mid:20010428005130.38527.qmail@web11002.mail.yahoo.com"><pre wrap=""></pre>
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Richard<br>
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